Centers of Triangles or Points of Concurrency. Geometry October 28, 2013. OBJECTIVE. You will learn how to construct perpendicular bisectors, angle bisectors, medians and altitudes of triangles constructed. Today’s Agenda. Triangle Segments Median Altitude Perpendicular Bisector
October 28, 2013
You will learn how to construct perpendicular bisectors, angle bisectors, medians and altitudes of triangles constructed
vertex to midpoint
What is NC if NP = 18?
MC bisects NP…so 18/2
If DP = 7.5, find MP.
7.5 + 7.5 =
Three – one from each vertex
The intersection of the medians is called the CENTRIOD.
They meet in a single point.
The length of the segment from the vertex to the centroid is twice the length of the segment from the centroid to the midpoint.
vertex to side cutting angle in half
5(x – 1) = 4x + 1
5x – 5 = 4x + 1
x = 6
The angle bisectors of a triangle are ____________.
The intersection of the angle bisectors is called the ________.
Point P is called the __________.
vertex to opposite side and perpendicular
The altitude is the “true height” of the triangle.
The altitudes of a triangle are concurrent.
The intersection of the altitudes is called the ORTHOCENTER.
midpoint and perpendicular
(don't care about no vertex)
Example 1: Tell whether each red segment is a perpendicular bisector of the triangle.
3x + 4
5x - 10
x = 7
The perpendicular bisectors of a triangle are concurrent.
The intersection of the perpendicular bisectors is called the CIRCUMCENTER.
PA = PB = PC
DA = 6
BA = 12
PC = 10
DP2 + 62 = 102
DP2 + 36 = 100
DP2 = 64
DP = 8
Tell if the red segment is an altitude, perpendicular bisector, both, or neither?
equidistant from vertices
equidistant from sides
2/3 distance from vertices to midpoint